Question 1196421
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LCM = lowest common multiple
GCF = greatest common factor


LCM formula:
LCM of x and y = (x*y)/(GCF of x and y)


The LCM of 5 and 8 is 5*8/1 = 40, where the GCF is 1
The LCM of 40 and 10 is 40*10/10 = 40, this time the GCF is 10


Overall, the LCM of the set {5,8,10} is 40
Let's multiply that by 1000
40*1000 = 40,000 
so that we have a possibly realistic gallon amount for the pool


Consider a pool with 40,000 gallons
Pump A working alone can empty the pool in 5 hours
The rate of this pump is (40,000)/5 = 8,000 gallons per hour


Pump B can empty it in 8 hours
The unit rate here is (40,000)/8 = 5,000 gallons per hour


Pump C can empty it in 10 hours
Unit rate = (40,000)/(10) = 4,000 gallons per hour


Add the three unit rates
A+B+C = 8000+5000+4000 = 17,000 gallons per hour


x = number of hours to empty the pool if the three pumps are used together


(unit rate)*(number of hours) = total amount drained
(17000 gallons per hour)*(x hours) = 40000 gallons
17000x = 40000
x = 40000/17000
x = 40/17
x = (34+6)/17
x = (34/17)+(6/17)
x = 2+(6/17)


It takes 2 whole hours, plus an additional 6/17 of an hour, to get the job done if the three pumps work together.


6/17 of an hour = (6/17)*60 = 21.17647 minutes approximately


If rounding to the nearest whole minute, then we get 22 minutes


So it takes about 2 hours, 22 minutes if the pumps work together (and no single pumps hinder any others).


Side notes:
2 hr + 22 min = 2*60+22 = 120+22 = 142 min
(40/17) hr = (40/17)*60 = 141.17647 = 142 min
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